if a pen runs out, it has no more ink left in it
Example: Luck which could continue indefinitely, or run out at any time.
if an official agreement or document runs out, it stops being legal at a certain date
Example: Many hospitals are running out of money.
if someone is run out in cricket, they have to stop hitting the ball and leave the field because the other team hits one set of stumps (=sticks) with the ball before they can reach it
Example: My contract runs out next July.
if something runs out, you do not have any more of it left
Example: Nevertheless, the money wouldn't last for ever, and then his luck would run out.
if time is running out, you do not have long to do something
Example: She desperately wanted to hold her son just once more, but after the endless hours of waiting she had run out of time.
to make a criminal or a person who you do not like leave a town
Example: The boys I knew when I was young and the men I've known since then... "I run out of steam.
to use all of something and not have any left
Example: They returned home from South Africa when their money ran out.